Constrained portfolio liquidation in a limit order book model

Order book resilience, price manipulations, and the. Problem p1 general portfolio optimization problem objective function. The model in which we limit the number of different assets held will be referred as cardinality constrained portfolio optimization problem problem p2. Optimal placement in a limit order book uc berkeley ieor.

Constrained portfolio liquidation in a limit order book model with and banach center publications 83, 925, 2008. S optimal execution and absence of price manipulations in limit order book models. Adaptive basket liquidation, finance and stochastics 10. We propose a continuoustime stochastic model for the dynamics of a limit order book. Unconstrained investing allows managers to pursue returns across. The liquidity price impact of market orders is described by an extension of a model for a limit order book with resilience that was proposed by obizhaeva and wang 2006. Liquidity risk, optimal portfolio liquidation, limit order book with resilience, call auction, market impact model, constrained trading strategies, market order. The impact of constraints on minimum variance portfolios.

Optimal execution strategies in limit order books with general shape functions. We consider a framework for solving optimal liquidation problems in limit order books. Research of the first two authors was supported by deutsche forschungsgemeinschaft through the research center matheon mathematics for key technologies. Order book resilience, price manipulations, and the positive. Due to the extreme time constraint in which a decision about market vs. Our paper, along with 7, is an attempt to use this model to tackle the completely di. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. Constrained portfolio liquidation in a limit order book model, preprint, qp lab and tu berlin. Optimal execution in a limit order book and an associated microstructure market impact model. We use a continuoustime modeling framework, but in contrast with previous related papers see e. In addition to classical frictionless markets and markets with transaction costs or bidask spreads, our framework covers markets with. Banach center publications warszawa 83 925 zeitschriftenartikel.

Optimal portfolio liquidation with execution cost and risk. Moallemi hua zheng may, 2015 abstract we model an electronic limit order book as a multiclass queueing system under. This paper addresses portfolio liquidation using a new angle. Modelling approaches for optimal liquidation under a limitorder book structure. Constrained portfolio liquidation in a limit order book. S optimal execution strategies in limit order books with general shape functions. In our model, the limit order book consists of a certain distribution of limit ask orders at prices. Market impact models and optimal trade execution 9th winter school on mathematical finance, lunteren 2010 references a.

Alexander schied school of orie, cornell university. In this paper we propose a dynamic model of limit order book lob. Alfonsi cermics, projet mathfi ecole nationale des ponts et chauss. This cited by count includes citations to the following articles in scholar. We study the optimal portfolio liquidation problem over a nite horizon in a limit order book with bidask spread and temporary market price impact penalizing speedy execution trades. A dynamic model of the limit order book researchgate. Alexander 2008 constrained portfolio liquidation in a limit order book model. S constrained portfolio liquidation in a limit order book model. Constrained portfolio liquidation in a limit order book model by aurelien alfonsi, antje fruth and alexander schied topics.

In this model, the absence of price manipulation in the sense of huberman and stanzl can easily be characterized by means of bochners theorem. This allows us to study the problem of minimizing the expected liquidation costs of an asset. Schied, alexander 2008 constrained portfolio liquidation in a limit order book model. The larger the number of shares he sells at this instant in time, the higher is the liquidity cost since his market order will be executed against the most favorable limit order prices in the book in a decreasing order. The reference price and the spreads are then combined to the offers limit orders i place. Optimal execution in a limit order book and an associated. Constrained portfolio liquidation in a limit order book model autorzy. Optimal execution cost for liquidation through a limit order. Schied, constrained portfolio liquidation in a limit order book model. We use a continuoustime modeling framework, but in contrast with previous related papers see, e.

The main feature of our model is that the shape of the lob is determined endogenously by an expected utility function via a competitive equilibrium argument. Order book resilience, price manipulation, and the. Optimal execution strategies in limit order books uzh. Order book resilience, price manipulation, and the positive.

Optimal basket liquidation for cara investors is deterministic. Limit order book a record of unexecuted limit orders maintained by the specialist. Constrained portfolio liquidation in a limit order book model alfonsi a. Liquidity risk, optimal portfolio liquidation, block trade execution, limit order book, market impact model, nonlinear price impact, order book resilience, market order 9. Constrained portfolio liquidation in a limit order book model. Preprint, forthcoming in banach center publications, tu berlin 2007. Optimal trade execution and absence of price manipulations in limit. Likewise, the constraints shifted the minimumvariance portfolios regional distributions closer to the benchmarks.

After having introduced the limit order book model, we specify the traders objectives in section 2. Optimal execution with nonlinear impact functions and trading enhanced risk. The model strikes a balance between three desirable features. Arbitrage and deflators in illiquid markets springerlink. We extend their model by allowing for a timedependent. The main characteristic of this model is that it does not explicitly consider the limit order book but statistically models liquidity. An investment style that does not require a fund or portfolio manager to adhere to a specific benchmark. Optimal trade execution and price manipulation in order books.

Kharroubi university paris 7 and crest istanbul workshop on mathematical finance may 19, 2009 huyen pham optimal portfolio liquidation. Optimal liquidation in a leveli limit order book for large tick stocks. The above described minimizing problem is easily solvable by the nonlinear quadratic programming methods. Assuming zero resilience, the resulting equilibrium density of the lob is random, nonlinear, and time inhomogeneous. Liquidity models in continuous and discrete time springerlink. Our model is a generalization of obizhaeva, wang 2005. A market impact model admits price manipulation if there is a round trip with negative expected liquidation costs. Dynamic equilibrium limit order book model and optimal. Therefore i need to model the reference price of the limit order book in the first step. A stochastic model for order book dynamics operations. In addition to classical frictionless markets and markets with transaction costs or bidask spreads, our. Then the bid and ask spread is calculated based on the volatity, drift, trade frequency and the inventory. We extend their model by allowing for a timedependent resilience rate, arbitrary trading times, and general equilibrium dynamics for the unaffected bid and ask prices. We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bidask spread and temporary market price impact penalizing speedy execution trades.

Limit order information system the electronic system supplying information about securities traded on participating exchanges so that the best securities prices can be found. These orders are treated equally with other orders in terms of priority of execution. Liquidity risk, optimal portfolio liquidation, limit order book with resilience, call auction, market impact model, constrained trading. This paper presents a stochastic model for discretetime trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. Download citation constrained portfolio liquidation in a limit order book model we consider the problem of optimally placing market orders so as to minimize the expected liquidity costs from. In such a model, gatheral 12 shows that exponential decay of market. The model does not assume the existence of a cash accountnumeraire. This allows us to study the problem of minimizing the expected liquidation costs of an asset position under. Optimal slippage for liquidation through a limit order market 4 transaction and the best ask price. Only perfectly negatively correlated assets portfolio margin constrained.

Optimal portfolio liquidation for cara investors munich. A dynamic model of the limit order book by ioanid rosu. Modelling approaches for optimal liquidation under a limit. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. Instead of focusing only on the scheduling aspect like almgren and chriss in j.